Electro-dynamic tether system stabilization in a circular orbit

Аuthors

Ledkov A. S.^*, Sobolev R. G.^**

Samara National Research University named after Academician S.P. Korolev, 34, Moskovskoye shosse, Samara, 443086, Russia

*e-mail: ledkov@inbox.ru
**e-mail: e-mail:r.g.sobolev@ya.ru

Abstract

The existence of technologies for strong materials production allows create extended space tether systems, which can be employed to solve a wide range of practical issues. Some projects imply the space tether system stabilization in a certain position. Stabilization can be realized by of the conductive cable interaction with the Earth electromagnetic field. The goal of the work consists in searching for the tether current control law, ensuring of the space tether system stabilization in a certain stationary state in a circular orbit. In contrast to the majority of existing works, the article considers the simultaneous stabilization of the system center of mass in a circular orbit and tether deflection angle stabilization in a certain stationary position.

A mathematical model of the cable system is described, and equations of motion using the second-kind Lagrange equations are obtained. In the framework of the assumptions made, the tether is considered as inelastic massless rod, and the bodies connected by it are material points. The model accounts for the attraction of the Earth and the Ampere force. A current in the electro-dynamic cable is considered as a control element. Control is sought as the sum of the programmed and stabilizing current force. It is shown that a limited set of program motions in a circular orbit can be implemented in the system. Equations of these motions are obtained. The stabilizing control is sought in the form of a linear dependence on generalized coordinates and velocities. The law of stabilizing control is sought in the form of a linear dependence on generalized coordinates and velocities. Selection of the control law parameters was performed using the Lyapunov theorem on asymptotic stability in the first approximation. Numerical simulation was executed to demonstrate the effectiveness of using an electrodynamic tether for the system stabilization in a circular orbit.

The results of the work may be employed while preparation of space programs involving of electro-dynamic tether systems implementation in a circular orbit.

Keywords:

electrodynamic tethered system, Lagrange equations, dipole model, Lyapunov method, stabilizing control

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